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What Is Poker Variance?

In poker, "variance" is shorthand for how much your results swing around your true win rate because of which cards come out. Statistically, the useful number is the standard deviation of your results, measured per session or per 100 hands. Once you know your average and your standard deviation, you can estimate how far your results could reasonably drift over the next 10, 100 or 1,000 sessions, and how many hands it takes before your win rate means much. This page shows how to get those numbers from your own results using the calculator above.

Worked Example: Eight Sessions in Buy-ins

A player records their net result for eight cash-game sessions, in buy-ins (+2.5 means they won two and a half buy-ins). These eight sessions are a sample of all the sessions they will ever play, so use the sample formula.

Data (buy-ins):2.5, −1, 4, −3.5, 1.5, 6, −2, 0.5

  1. Mean. x̄ = 8 / 8 = 1
  2. Deviations and squares. Subtract the mean from each value and square the result:
xᵢxᵢ − x̄(xᵢ − x̄)²
2.51.52.25
−1−24
439
−3.5−4.520.25
1.50.50.25
6525
−2−39
0.5−0.50.25
Sum070
  1. Sum of squares. Σ(xᵢ − x̄)² = 70
  2. Sample variance. s² = 70 / (8 − 1) = 10; sample standard deviation s = √10 = 3.1623

Sample variance s² = 70 / 7 = 10, so the standard deviation is s ≈ 3.162 buy-ins per session against an average of +1 buy-in. A single session tells you very little: the swing is about three times the average result.

Formula

Two formulas do most of the work. The first is ordinary sample standard deviation; the second scales it to a longer stretch of play.

Standard Deviation per Session

s = √[ Σ(xᵢ − x̄)² / (n − 1) ]
  • xᵢResult of session i (in buy-ins, or bb per 100 hands)
  • x̄Your average result per session
  • nNumber of sessions recorded

Spread After k More Sessions

SD of total = s × √k
  • kNumber of future sessions
  • x̄ × kExpected total after k sessions

How to Work Out Your Poker Variance

  1. Record results in a consistent unit.Use buy-ins per session, or big blinds per 100 hands. Do not mix stakes without converting.
  2. Enter them in the calculator (Sample mode).Your recorded sessions are a sample of all the sessions you will play.
  3. Note the mean and standard deviation.The mean is your observed win rate; the standard deviation is your swing per session.
  4. Scale to the horizon you care about.Over k sessions, expect a total of mean × k with a standard deviation of SD × √k.
  5. Read off a range.Roughly 95% of outcomes fall within two of those standard deviations of the expected total.

Using the Numbers

1Expected Range Over the Next 25 Sessions

Data:Mean = +1 buy-in per session, s ≈ 3.162 (from the worked example), k = 25
Solution:Expected total = 1 × 25 = 25 buy-ins. SD of the total = 3.162 × √25 ≈ 15.81 buy-ins.
Answer:About 95% of 25-session stretches end between −6.6 and +56.6 buy-ins (25 ± 2 × 15.81)

2Chance of Being Down After 25 Sessions

Data:Expected +25 buy-ins, SD of total ≈ 15.81 buy-ins
Solution:z = (0 − 25) / 15.81 ≈ −1.58. From the normal distribution, P(Z < −1.58) ≈ 0.057.
Answer:Roughly a 6% chance of being behind after 25 sessions, if +1 buy-in per session is the true win rate

How to Use This Calculator for Poker Results

The calculator works on any list of results:

  1. Export or copy your session results (or results per 100 hands) from your tracker or notes.
  2. Paste them in, one result per line or separated by commas. Use minus signs for losing sessions.
  3. Set the mode to Sample and read the mean (your observed win rate) and standard deviation.
  4. Use the √k rule above to turn the per-session standard deviation into a range for a longer stretch.

What This Tells You

  • Whether a losing stretch is within the normal range for your game or a sign of a real problem.
  • How many sessions you need before your observed win rate is a reliable guide.
  • A realistic basis for bankroll decisions, instead of a gut feeling.

Common Questions Poker Players Answer With This

Downswings

Is losing 15 buy-ins over 25 sessions unusual for my win rate and standard deviation?

Sample size

How many hands until my win rate is trustworthy to within a few bb/100?

Game selection

Comparing the swings of two formats or stakes using your own results.

Bankroll planning

How big a bankroll keeps the chance of going broke acceptably low.

Things to Keep in Mind

These numbers are estimates built on your own history, with the usual caveats:

Your mean is itself uncertain

After 8 sessions, the margin of error on your average is about 2 × 3.162 / √8 ≈ 2.2 buy-ins, more than twice the +1 buy-in average itself. Treat early win rates with suspicion.

Sessions are not all the same length

Results per 100 hands are more comparable than results per session, because session length varies.

The normal approximation is rough

Tournament results in particular are very skewed (many small losses, rare big wins), so ranges based on the normal distribution are less reliable there.

Your game changes

Moving up in stakes or changing style changes both your win rate and your standard deviation. Recalculate from recent results.

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자주 묻는 질문: 포커 차이 계산기

분산에 대해 알아야 할 모든 것.

포커에서 분산이란 무엇입니까?

포커의 차이는 결과의 통계적 변동을 측정합니다. 긍정적인 승률이 있더라도 카드 배포의 ��질적인 무작위성으로 인해 단기 결과가 크게 변동될 수 있습니다. 높은 분산은 결과가 짧은 기간 동안 예상 값(EV)에서 크게 벗어날 것임을 의미합니다. 포커 분산을 이해하면 불운(분산)과 나쁜 플레이(부정적 EV)를 구별하는 데 도움이 됩니다.

차이가 포커 승률에 어떤 영향을 미치나요?

차이는 실제 승률을 변경하지 않으며 유한�� 샘플에 대한 관측 결과에 영향을 미칩니다. 5bb/100 핸드를 획득한 플레이어는 변동으로 인해 10bb/100을 잃거나 20bb/100을 획득하는 경험을 할 수 있습니다. 게임 형식(예: 토너먼트 대 현금 게임)의 차이가 높을수록 관찰된 결과가 실제 승률에 수렴되기 전에 더 많은 핸드가 필요합니다.

How many hands do I need before my win rate is reliable?

The 95% margin of error on your win rate is about 1.96 × SD / √(hands / 100), in bb/100. With an SD of 75 bb/100, the margin is ±14.7 bb/100 after 10,000 hands and still ±4.6 bb/100 after 100,000 hands. To be 95% confident that a 5 bb/100 win rate is above zero you need roughly 86,000 hands (1.96 × 75 / 5 = 29.4, and 29.4² × 100 = 86,436).

어떤 포커 형식이 가장 높은 차이를 보입니까?

토너먼트(MTT)는 대부분의 상금이 상위에 집중되어 있기 때문에 변동성이 가장 높습니다. Sit & Go에는 중간 정도의 변동이 있습니다. 캐시 게임(특히 풀링)은 분산이 가장 낮습니다. 캐시 게임 내에서는 스택이 깊고 공격적인 플레이 스타일이 많을수록 변동성이 커집니다. PLO(Pot-Limit Omaha)는 에퀴티 런아웃이 가까워서 홀덤보다 변동성이 더 높습니다.

How do I calculate my poker standard deviation?

1. Record your result for each block of 100 hands (or each session). 2. Find the average. 3. Square each block's difference from the average. 4. Add them, divide by the number of blocks minus 1, and take the square root. Figures of roughly 60–100 bb/100 are often quoted for No-Limit Hold'em cash games, but your own number depends on your game and style, so calculate it from your own results.

How likely is a losing stretch for a winning player?

Treat the total over many hands as roughly normally distributed. For a 3 bb/100 win rate and an SD of 80 bb/100, 10,000 hands is 100 blocks of 100: expected result = 3 × 100 = +300 bb, standard deviation = 80 × √100 = 800 bb. The chance of being behind after those 10,000 hands is P(Z < −300 / 800) = P(Z < −0.375) ≈ 35%. Bankroll management exists to survive stretches like this.